The original motivation for writing this book was to develop the background
which is needed for an appropriate understanding of the quadratic cost minimization
problem (and its indefinite minimax version). However, due to page
and time limitations, I have not yet been able to include any optimal control in
this volume (only the background needed to attack optimal control problems).
The book on optimal control still remains to be written.
Not only was it difficult to decide exactly what parts of the existing theory
to include, but also in which form it should be included. One such decision
was whether to work in a Hilbert space or in a Banach space setting. Optimal
control is typically done in Hilbert spaces. On the other hand, in the basic theory
it does not matter if we are working in a Hilbert space or a Banach space (the
technical differences are minimal, compared to the general level of difficulty of
the theory).

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2005
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